Kelemen-style MLT small mutation range question

[zsolnai]

Hello there everyone,

I believe LuxRender and SLG2 (pathgpu2) uses the Kelemen-Szirmay style Metropolis light transport algorithm.

In samplers/metrosampler.cpp line 94
and luxrays\samples\smallluxgpu2\pathocl\kernels\pathocl_kernel_samplers.cpp (around) line 193 I have found this:

Code: Select all

const float dx = s1 / (s1 / s2 + fabsf(2.f * randomValue - 1.f)) - s1 / (s1 / s2 + 1.f);

Two questions:
- is this formula a linear approximation for the s2*exp(-log(...)...) term in the Kelemen paper? [1]
- using the term fabsf(...) instead of randomValue itself is a convolution for the randomValue to alter the distribution?

Also, may I ask how far this implementation is (generally) from the original Kelemen paper?

[1] http://www.iit.bme.hu/~szirmay/paper50_electronic.pdf

[Dade]

I believe LuxRender and SLG2 (pathgpu2) uses the Kelemen-Szirmay style Metropolis light transport algorithm.

Yes, however LuxRender has lazy evaluation and QMC for image coordinates sampling (SLG doesn't).

In samplers/metrosampler.cpp line 94
and luxrays\samples\smallluxgpu2\pathocl\kernels\pathocl_kernel_samplers.cpp (around) line 193 I have found this:

Code: Select all

const float dx = s1 / (s1 / s2 + fabsf(2.f * randomValue - 1.f)) - s1 / (s1 / s2 + 1.f);

Two questions:
- is this formula a linear approximation for the s2*exp(-log(...)...) term in the Kelemen paper? [1]

Yes and it is a lot faster to compute than exp/log.

- using the term fabsf(...) instead of randomValue itself is a convolution for the randomValue to alter the distribution?

It is the same of "if (random() < 0.5) { ...}" pesudo-code at page 7 on Kelemen-Szirmay's paper.

May I ask how far this implementation is (generally) from the original Kelemen paper?

For what I know, LuxRender has a complete implementation of Kelemen's paper plus QMC image sampling. SLG is about the same code but without lazy evaluation (I think it something really inefficient to run a GPU) and QMC.

[Lord Crc]

- using the term fabsf(...) instead of randomValue itself is a convolution for the randomValue to alter the distribution?

It is the same of "if (random() < 0.5) { ...}" pesudo-code at page 7 on Kelemen-Szirmay's paper.

But you still have the < 0.5 bit there, so why the abs? What am I missing?